when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.
We have,
Absolute value:
The absolute value of a number represents its distance from zero on the number line. It is always a non-negative value.
For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3.
|x - 5|:
In this expression, we have the absolute value of the quantity (x - 5).
It means that we are looking at the distance between x and 5 on the number line.
x < 5:
The condition x < 5 states that x is less than 5.
It means that x is located to the left of 5 on the number line.
Simplification:
When x is less than 5, it implies that x is located to the left of 5.
In this case,
The quantity (x - 5) becomes negative because we are subtracting a larger value (5) from a smaller value (x).
Now,
The expression |x - 5| can be simplified to -(x - 5), which means taking the negation of (x - 5).
- If x = 3, which is less than 5, we can substitute it into the expression:
|x - 5| = |3 - 5| = |-2| = 2
- If x = 7, which is greater than 5:
|x - 5| = |7 - 5| = |2| = 2
In both cases,
The value of |x - 5| is 2.
However, when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.
Thus,
when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.
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1.
Find the surface area of the right cone.
Round your answer to the nearest
hundredth.
22 ft
8 ft
Answer:
789.40 square feet (to nearest hundredth)
Step-by-step explanation:
surface area = area of circular base + curved surface area
= πr² + πrL, where L is length of sloped edge.
using Pythagoras' Theorem, L² = 22² + 8² = 548.
L = 2√137 (do not round the answer yet, keep it in this form).
surface area = πr² + πrL
= π(8)² + π(8)(2√137)
= 789.40 square feet (to nearest hundredth)
Show that the equations x+y+z = 4, 2x+5y-2z =3, x+7y-7z =5 are not consistent
Answer:
We can start by using the second equation to eliminate x:
2x + 5y - 2z = 3
2x = -5y + 2z + 3
x = (-5/2)y + z + 3/2
Now we can substitute this expression for x into the first and third equations:
x + y + z = 4
(-5/2)y + z + 3/2 + y + z = 4
(-5/2)y + 2z = 5/2
x + 7y - 7z = 5
(-5/2)y + z + 3/2 + 7y - 7z = 5
(9/2)y - 6z = 7/2
Now we have a system of two equations with two variables, (-5/2)y + 2z = 5/2 and (9/2)y - 6z = 7/2. We can use any method to solve for y and z, such as substitution or elimination. However, we will find that the system is inconsistent, meaning there is no solution that satisfies both equations.
Multiplying the first equation by 9 and the second equation by 5 and adding them, we get:
(-45/2)y + 18z = 45/2
(45/2)y - 30z = 35/2
Adding these two equations, we get:
-12z = 40/2
-12z = 20
z = -5/3
Substituting z = -5/3 into (-5/2)y + 2z = 5/2, we get:
(-5/2)y + 2(-5/3) = 5/2
(-5/2)y - 10/3 = 5/2
(-5/2)y = 25/6
y = -5/12
Substituting y = -5/12 and z = -5/3 into any of the original equations, we get:
x + y + z = 4
x - 5/12 - 5/3 = 4
x = 29/12
Therefore, the solution is (x, y, z) = (29/12, -5/12, -5/3). However, if we substitute these values into any of the original equations, we will find that it does not satisfy the equation. For example:
2x + 5y - 2z = 3
2(29/12) + 5(-5/12) - 2(-5/3) = 3
29/6 - 5/2 + 5/3 ≠ 3
Since there is no solution that satisfies all three equations, the system is inconsistent.
Step-by-step explanation:
Answer:
See below for proof.
Step-by-step explanation:
A system of equations is not consistent when there is no solution or no set of values that satisfies all the equations simultaneously. In other words, the equations are contradictory or incompatible with each other.
Given system of equations:
[tex]\begin{cases}x+y+z = 4\\2x+5y-2z =3\\x+7y-7z =5\end{cases}[/tex]
Rearrange the first equation to isolate x:
[tex]x=4-y-z[/tex]
Substitute this into the second equation to eliminate the term in x:
[tex]\begin{aligned}2x+5y-2z&=3\\2(4-y-z)+5y-2z&=3\\8-2y-2z+5y-2z&=3\\-2y-2z+5y-2z&=-5\\5y-2y-2z-2z&=-5\\3y-4z&=-5\end{aligned}[/tex]
Subtract the first equation from the third equation to eliminate x:
[tex]\begin{array}{cccrcrcl}&x&+&7y&-&7z&=&5\\\vphantom{\dfrac12}-&(x&+&y&+&z&=&4)\\\cline{2-8}\vphantom{\dfrac12}&&&6y&-&8z&=&1\end{aligned}[/tex]
Now we have two equations in terms of the variables y and z:
[tex]\begin{cases}3y-4z=-5\\6y-8z=1\end{cases}[/tex]
Multiply the first equation by 2 so that the coefficients of the variables of both equations are the same:
[tex]\begin{cases}6y-8z=-10\\6y-8z=1\end{cases}[/tex]
Comparing the two equations, we can see that the coefficients of the y and z variables are the same, but the numbers they equate to is different. This means that there is no way to add or subtract the equations to eliminate one of the variables.
For example, if we subtract the second equation from the first equation we get:
[tex]\begin{array}{crcrcl}&6y&-&8z&=&-10\\\vphantom{\dfrac12}-&(6y&-&8z&=&\:\:\;\;\:1)\\\cline{2-6}\vphantom{\dfrac12}&&&0&=&-11\end{aligned}[/tex]
Zero does not equal negative 11.
Since we cannot eliminate the variable y or z, we cannot find a unique solution that satisfies all three equations simultaneously. Therefore, the system of equations is inconsistent.
Sandra is traveling 15 mph on her bicycle. After 4 hours, how far will she have traveled?
Answer:
→ 15m/hr * 4hr = 60! ←
Hope This Helps On You're Quiz/Assignment
A company produces and sells solar panels for $520. The company's daily profit, P(x), can be modeled by the function P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. Use the graph to answer the questions. Graph of function p of x equals negative 6 x squared plus 156 x plus 1,000. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 1000), increases to the vertex at about (13, 2014), and decreases through about (31, 0). Part A: Identify the approximate value of the y-intercept. Explain what the y-intercept means in terms of the problem scenario. (3 points) Part B: Identify the approximate value of the x-intercept. Explain what the x-intercept means in terms of the problem scenario. (3 points) Part C: Identify the approximate value of the maximum of the function. Explain what the maximum of the function means in terms of the problem scenario. (4 points)
The maximum daily profit the company can earn is $2,350.
It is a set of points in a coordinate plane that represents the values of the function for different inputs.
The function P(x) = −6x² + 156x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.
Therefore, the maximum daily profit the company can earn is $2,350.
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Find u if a normal distribution has a standard deviation of 3.5 with a z-score of -0.74 for a value of 6.2
Answer:
8.79-------------------
Use the formula for z-score
z = (x - μ) / σSubstituting the given values, we get:
-0.74 = (6.2 - μ) / 3.5Solve it for mean μ:
-0.74 * 3.5 = 6.2 - μ -2.59 = 6.2 - μ μ = 6.2 - (-2.59) μ = 8.79Therefore, the mean of the normal distribution is 8.79.
5) El precio del petróleo en los dos últimos días tuvo las siguientes fluctuaciones: aumentó un 3,5% en
el primer día y luego bajó un 2% en el último día. Si el valor final es de U$S 68, ¿cuál era el valor
inicial?
Answer:
5) El precio del petróleo en los dos últimos días tuvo las siguientes fluctuaciones: aumentó un 3,5% en el primer día y luego bajó un 2% en el último día. Si el valor final es de U$S 68, ¿cuál era el valor inicial?
La solución al problema matemático es la siguiente:
Supongamos que el valor inicial del petróleo es x. En el primer día, el precio aumentó en un 3,5%, por lo que el nuevo precio es x + 0.035x = 1.035x. En el segundo día, el precio disminuyó en un 2%, por lo que el precio final es 1.035x - 0.02(1.035x) = 0.98(1.035x) = 1.0143x.
Dado que sabemos que el precio final es de U$S 68, podemos establecer una ecuación para resolver x: 1.0143x = 68.
Resolviendo para x, obtenemos x = 68/1.0143 ≈ U$S 67.04.
Entonces, el valor inicial del petróleo era aproximadamente U$S 67.04.
MARCA COMO CEREBRO!!!
if a circle has a radius of 10 cm and the measure of arc AB is 45 degrees, find the length of the arc AB
Answer:
[tex]\huge\boxed{\sf S= 7.85 \ cm}[/tex]
Step-by-step explanation:
Given:arc AB = θ = 45 degrees
Radius = r = 10 cm
π = 3.14
Required:Length = S = ?
Formula:[tex]\displaystyle S= \frac{\theta}{360} \times 2 \pi r[/tex]
Solution:Put the given data in the formula.
Finding arc length.
[tex]\displaystyle S = \frac{45}{360} \times 2(3.14)(10)\\\\S = 0.125 \times 62.8\\\\S= 7.85 \ cm\\\\\rule[225]{225}{2}[/tex]
Can someone find x and y pls
Answer: x = 101, y = 20
From corresponding angles, as both pairs of lines are parallel, we know that 79 is the supplement of x. That means 79 + x = 180.
From this we have x = 101 degrees.
From corresponding angles, x is the supplement of ( 4y - 1 )
Since we know x = 101, we can plug it into our equation:
4y - 1 + 101 = 180
Simplifying:
4y + 100 = 180
Subtracting 100 from both sides of the equation:
4y = 80
Dividing by 4:
y = 20
Hope this helps!
factorise fully
1) x²y - 5yx - 6y
2) w² (a - b) - 9 (a - b)
please help
solve for x solution will be in decimal form
Answer:
x = -0.25
Step-by-step explanation:
You want to solve for x when corresponding sides of the similar triangles have lengths 6 and 15, and (2x -3) and (3x -8).
ProportionCorresponding sides are proportional in similar triangles, so we have ...
(2x -3)/6 = (3x -8)/15
5(2x -3) = 2(3x -8) . . . . . . multiply by 30
10x -15 = 6x -16 . . . . . . simplify
4x = -1 . . . . . . . . . . . . add 15-6x
x = -0.25
The value of x is -0.25.
__
Additional comment
This negative value of x gives side length ratios in the two triangles of -7/12. Negative side lengths of -3.50 and -8.75 make no sense geometrically. The proportion is satisfied, but the figure cannot be drawn with a negative side length.
<95141404393>
Kathy had of a pepperoni pizza in
her refrigerator. She gave her friend
a slice that was of the original pizza.
How much pizza does Kathy have left?
The answer is she has 7/8 (or seven slices) of the pizza left. Based on the information given, we can calculate that Kathy ate 1/8 (or one slice) of the original pepperoni pizza.
It is important to note that the size of the original pizza is unknown, so we cannot accurately determine the exact amount of pizza Kathy has left in terms of square inches or centimeters.
However, we do know that she has the majority of the pizza remaining, and could potentially have enough for multiple meals or leftovers. Additionally, if Kathy is tracking her caloric intake, she can calculate the number of calories consumed from the slice she ate and adjust her diet accordingly.
Overall, it seems like Kathy has a decent amount of pizza left to enjoy
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Question Number 16 of 20 - Geometry
In square ABCD, AC = 32-4 and BE = x + 6, where E is the intersection of the diagonals.
What is the length of AC?
16
11
D
44
22
The length of AC is 28. so none of the given options is correct.
In square ABCD, AC represents the length of one side of the square. The given information states that AC is equal to 32-4.
To calculate AC, we subtract 4 from 32:
AC = 32 - 4
AC = 28
Therefore, the length of AC is 28. None of the provided options match this result, so none of the given options is correct.
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Triangles MNO and JKL below are congruent. If m<M =40c, m<N =120c, and m<O =20c, whats m<L? a. 120° b. 20° c. 40° d. 70°
Answer: b, 20°
Step-by-step explanation: Since triangles MNO and JKL are congruent, we know that all of their corresponding angles are congruent. This means that m<L = m<O = 20°
please look at the picture
6x-7y=-10
12x-5=16
2xay=10
-10+16+x=10
10=-10+16+x=6x
6x+10=16x
ay=16x
Issa puts
dollars into an investment with an interest rate of 4 percent per year and
dollars into an investment with an interest rate of 10 percent per year. She invests a total of $5900, and her interest earnings after one year are $434. From this information, we can create two equations: one for the total investment and one for the interest earned. State both equations, and then solve the system to determine how much Issa invested in each.
The equation that describes the total investment is
The equation that describes the interest earned is
Amount invested at 4 percent interest is $
Amount invested at 10 percent interest is $
Issa invested $2600 at a 4 percent interest rate and $3300 at a 10 percent interest rate.
Let's assume Issa invests x dollars at a 4 percent interest rate and y dollars at a 10 percent interest rate.
The equation that describes the total investment is:
x + y = 5900
The equation that describes the interest earned is:
0.04x + 0.1y = 434
To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.
From the first equation, we can express x in terms of y:
x = 5900 - y
Substituting this value of x into the second equation, we have:
0.04(5900 - y) + 0.1y = 434
Now, let's solve this equation to find the value of y:
0.04(5900 - y) + 0.1y = 434
236 - 0.04y + 0.1y = 434
0.06y = 198
y = 198 / 0.06
y = 3300
Now that we have the value of y, we can substitute it back into the first equation to find x:
x + 3300 = 5900
x = 5900 - 3300
x = 2600
Therefore, Issa invested $2600 at a 4 percent interest rate and $3300 at a 10 percent interest rate.
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Please, someone help me with this answer, I really would appreciate it so much. Show all work. Recall the formula: A = P(1 + 2)² nt Mark invests $7,938 in a retirement account with a fixed annual interest rate of 2% compounded semiannually. What will the account balance be after 19 years
The account balance will be approximately $11,390 after 19 years.
In this case, Mark invests $7,938 with an annual interest rate of 2% compounded semiannually. Therefore:
P = $7,938
r = 2% = 0.02 (as a decimal)
n = 2 (compounded semiannually)
t = 19 years
Plugging these values into the formula, we have:
[tex]A = \$7,938(1 + 0.02/2)^{(2*19)[/tex]
Calculating the expression inside the parentheses:
(1 + 0.02/2) = 1.01
Raising this to the power of (2*19):
[tex](1.01)^{(2*19)} = 1.43[/tex]
Multiplying this by the principal amount:
A ≈ $7,938 * 1.43
A ≈ $11,390
Therefore, the account balance will be approximately $11,390 after 19 years.
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15% will last how long when the battery discharge rate is 0.12% in 30 seconds
37.5 seconds is equivalent to 0.625 minutes for the battery to discharge from 15% to 0% with a discharge rate of 0.12% every 30 seconds.
To calculate how long a battery will last when it discharges at a rate of 0.12% per 30 seconds, we can set up a proportion based on the given information.
Let's assume the battery has a total charge of 100%. We want to find out how long it takes for the battery to discharge from 15% to 0%, given a discharge rate of 0.12% every 30 seconds.
First, let's determine the proportion:
(0.12% / 30 seconds) = (15% / x sec
To solve for x (the time it takes for the battery to discharge from 15% to 0%), we can cross-multiply:
0.12% × x = 30 seconds × 15%
Now, let's solve for x:
0.0012 × x = 0.3 × 15%
0.0012 × x = 0.045
Divide both sides by 0.0012:
x = 0.045 / 0.0012
x ≈ 37.5
Therefore, it would take approximately 37.5 seconds for the battery to discharge from 15% to 0% with a discharge rate of 0.12% every 30 seconds.
To convert 37.5 seconds into minutes, we divide the number of seconds by 60 (since there are 60 seconds in a minute).
37.5 seconds / 60 = 0.625 minutes
Therefore, 37.5 seconds is equivalent to 0.625 minutes.
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What is the intermediate step in the form
(x+a)^2=b as a result of completing the square for the following question
The intermediate step in completing the square is[tex]$x^2 + 2ax + (a^2) = b - a^2 + (a^2)$[/tex]
To complete the square for the equation [tex]$(x+a)^2=b$[/tex], we can follow these steps:
1. Expand the left side of the equation: [tex]$(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$[/tex].
2. Rewrite the equation by isolating the squared term and the linear term: [tex]$x^2 + 2ax = b - a^2$[/tex].
3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:
[tex]$x^2 + 2ax + (a^2) = b - a^2 + (a^2)$[/tex].
4. Simplify the right side of the equation: [tex]$x^2 + 2ax + (a^2) = b$[/tex].
This step can be represented as: [tex]\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\][/tex]
This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.
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y is inversely proportional to the square root of x. y=5 when x=36. find a formula linking x and y.
Answer:
y = 30/√x
Step-by-step explanation:
y = k/√x (where k is a constant).
5 = k/√36
5 = k/6
5 X 6 = k
k = 5 X 6 = 30.
y = 30/√x
The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. Which measurement is closet to the length of this rectangle in feet?
The length of the rectangle is about 12.37 feet.
We are given that;
Width= 4 feet
Diagonal length= 13feet
Now,
The width and length of the rectangle are the legs and the diagonal is the hypotenuse. We can label them as:
w = 4 (width) l = ? (length) d = 13 (diagonal)
Plugging these values into the Pythagorean theorem, we get:
w^2 + l^2 = d^2 4^2 + l^2
= 13^2 16 + l^2 = 169
l^2 = 169 - 16
l^2 = 153
l = √(153)
l ≈ 12.37
Therefore, by Pythagoras theorem the answer will be 12.37 feet.
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A 500g packet of beans costs £1.55. A 125g packet of the same beans costs £0.36. Which packet is better value for money?
Step-by-step explanation:
Find unit cost per gram for each packet....lower unit cost is better value
L 1.55 / 500 g = .0031 L/g
L .36 / 125 g = .0029 L/g <=======best value 125 g packet
What would be the Prefix notation for the given equation?
(a+(b/c)*(d^e)-f)
a.
-+a*b/c^def
b.
-a+*/bc^def
c.
-+a*/^bcdef
d.
-+a*/bc^def
The Prefix notation for the given equation is "[tex]\pm a \times /bc^{de}^f[/tex]". d.
The Prefix notation for the given equation "[tex](a+(b/c) \times (d^e)-f)[/tex]" would be:
[tex]\pm a \times /bc^{de}^f[/tex]
In Prefix notation, also known as Polish notation, the operators come before their operands.
Here's a step-by-step breakdown of converting the given equation to Prefix notation:
Start with the given equation: (a+(b/c)*(d^e)-f)
Replace the arithmetic operators with their corresponding symbols in Prefix notation:
Addition (+) becomes +
Division (/) becomes /
Exponentiation (^) becomes ^
Subtraction (-) becomes -
Rearrange the equation to move the operators before their operands:
Replace [tex](a+(b/c)(d^e)-f)[/tex] with [tex](\pm a/bc^{de}^f)[/tex]
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Write the expression for the following statement without
any spaces: the quantity 5 plus 3z, to the 8th
power less than 9b divided by 7
can be expressed as
The inequality expression for the sentence in this problem is given as follows:
[tex](5+3z)^8 < \frac{9b}{7}[/tex]
How to represent the sentence?The sentence in the context of this problem is defined as follows:
"quantity 5 plus 3z, to the 8th power less than 9b divided by 7"
The first quantity, 5 plus 3z, to the 8th power, is expressed as follows:
[tex](5 + 3z)^8[/tex]
The second quantity, 9b divided by 7, is given as follows:
9b/7.
The inequality symbol for the word less is given as follows:
<.
Hence the inequality is given as follows:
[tex](5+3z)^8 < \frac{9b}{7}[/tex]
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Can anyone help me solve this question?
x = e^y
Step-by-step explanation:
Pick any point on the graph below for a solution:
Fill in the missing digit to make the least number that satisfies the condition (makes it
a true statement).
234.... is divisible by 3.
TYSM 4 UR HELP
(If you get it right I will give you Brainiest )
what is the following term of -3;0;3;6.
Step-by-step explanation:
Start at -3 then begin adding 3's to get the next terms
-3 0 3 6 9 .....
Please help i need help on pre-calc
Answer:
32.5 square units
Step-by-step explanation:
Area of triangle = ½ ab sin C
where a and b are to sides that meet at angle C.
Area of triangle = ½ (13)(10) sin 150
= 32.5 square units.
please see attachment for a visual
Can someone help me please
In the given diagram, we have a triangle with two angles labeled as (3x + 10)° and (4x - 30)°. We need to solve for the value of x.
To find the value of x, we can use the property that the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the equation:
(3x + 10) + (4x - 30) + 90 = 180
Let's simplify the equation step by step:
Combine like terms:
3x + 4x + 10 - 30 + 90 = 180
7x + 70 = 180
Next, isolate the variable term by subtracting 70 from both sides:
7x + 70 - 70 = 180 - 70
7x = 110
To solve for x, divide both sides of the equation by 7:
(7x)/7 = 110/7
x = 15.71
Therefore, the value of x is approximately 15.71.
Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.
Which equation gives the number of 13
inches that are in 56
inch?
CLEAR CHECK
13÷56=25
56÷13=518
13÷56=185
56÷13=52
Step-by-step explanation:
The answer is 5/6 ÷ 1/3 = 5/18
because
5/6 × 1/3 = 5/18 and it's true
I’m confused on this, help. Thanks you all. : )
Answer: There is no solution to this problem.
Step-by-step explanation:
The goal test score pints are 150, 103, and 41. Let's check to see if each statement is true
A. The total points for the tests are:
Type A - 156
Type B - 98
Type C - 40
None of these matches the total points.
B. The total points for the tests are:
Type A - 39
Type B - 98
Type C - 160
None of these matches the total points.
C.
Type A - 156
Type B - 2,352
Type C - 40
None of these matches the total points.
Since none of these statements match this data, there is no solution to this chart. Hope this helps!
-From a 5th Grade Honors Student